Estimation of Labyrinth Weir Discharge coefficient using Self-Adaptive Extreme Learning Machine

Abstract

For the first time, in the current study, the discharge coefficient of labyrinth weirs was simulated using the Self-Adaptive Extreme Learning Machine (SAELM) artificial intelligence model in both cases including normal orientation labyrinth weirs (NLWs) and inverted orientation labyrinth weirs (ILWs). The Monte Carlo simulations were also implemented to evaluate the accuracy of the artificial intelligence model. In addition, the validation of the numerical model results was carried out by means of the k-fold cross validation approach. In this study, k was considered equal to 5. First, the most optimized neuron of the hidden layer was computed. The number of the hidden layer neurons was calculated 30. Also, by analyzing the results of different activation functions, it was concluded that the sigmoid activation function has higher accuracy than others. After that, the superior model was identified by conducting a sensitivity analysis. The superior model estimated the discharge coefficient values in terms of all input parameters. This model approximated discharge coefficient values of labyrinth weirs with reasonable accuracy. For example, the values of R2, the Scatter Index and the Nash–Sutcliffe efficiency coefficient for the superior model were calculated 0.966, 0.034 and 0.964, respectively. In addition, the ratio of the total head above the weir to the height of the weir crest (HT/P) and the ratio of length of apex geometry to width of a single cycle (A/w) were identified as the most effective parameters. Finally, a partial derivative sensitivity analysis (PDSA) was conducted for the input parameters.